Shear-horizontal wave (SH wave)

A shear-horizontal wave propagating in the $x$ direction has displacement perpendicular to the sagittal $xy$ plane, for example $\mathbf{u}=w(x,y,t){\mathbf{e}}_z$. It is divergence-free and obeys the scalar shear-wave equation $w_{tt}=c_S^2(w_{xx}+w_{yy})$.

Between parallel boundaries, a guided shear-horizontal mode has a discrete transverse wavenumber $q_n$ and dispersion relation ${\omega }_n^2=c_S^2(k^2+q_n^2)$. Its cutoff frequency is $c_S{q}_n$.